Impact of Operating Conditions on Linear ARX Models for Air Source Heat Pumps

Abstract

Linear black-box models are widely used for control-oriented modelling of air source heat pumps, but their prediction accuracy depends on the operating conditions under which they are identified. This paper analyses the operating-point dependency of low-order linear Auto-Regressive with exogenous input (ARX) models for a variable-speed air-source heat pump. Using simulation data generated from a detailed vapour compression cycle model, separate ARX (2,2,0) models are identified around four compressor speed operating points (30, 60, 90, and 120 Hz) using a consistent excitation and identification framework. Model performance is evaluated on validation datasets with respect to electrical power consumption, thermal capacity, and cooling capacity. The results show that electrical power consumption is predicted with consistently high accuracy across all operating points, with validation FIT values exceeding 95%. Thermal and cooling outputs exhibit stronger operating-point dependency, with reduced accuracy at low compressor speed and validation FIT values above 90% at medium and high speeds when bounded relative excitation is applied. The findings demonstrate that the accuracy of linear ARX models is strongly influenced by operating regime and excitation design rather than by model structure alone, and confirm that compact locally identified linear models remain suitable for control-oriented heat-pump applications.